### multi_elem

Run Example
```(%i1)? multi_elem;

-- Function: multi_elem (<l_elem>, <multi_pc>, <l_var>)
decomposes a multi-symmetric polynomial in the multi-contracted
form <multi_pc> in the groups of variables contained in the list
of lists <l_var> in terms of the elementary symmetric functions
contained in <l_elem>.

(%i1) multi_elem ([[2, e1, e2], [2, f1, f2]], a*x + a^2 + x^3,
[[x, y], [a, b]]);
3
(%o1)         - 2 f2 + f1 (f1 + e1) - 3 e1 e2 + e1
(%i2) ratsimp (%);
2                       3
(%o2)         - 2 f2 + f1  + e1 f1 - 3 e1 e2 + e1

Other functions for changing bases: `comp2ele'.

(%o1)                                true
(%i2) ```
Run Example
```multi_elem ([[2,e1,e2],[2,f1,f2]],x+y+u+v,[[x,y],[u,v]]);
resolvante
generale

NOTE: To compile the system do
define: warning: redefining the built-in function resolvante_produit_sym
define: warning: redefining the built-in function resolvante_unitaire
define: warning: redefining the built-in function resolvante_alternee1
define: warning: redefining the built-in function resolvante_klein
define: warning: redefining the built-in function resolvante_klein3
define: warning: redefining the built-in function resolvante_vierer
define: warning: redefining the built-in function resolvante_diedrale
define: warning: redefining the built-in function resolvante_bipartite
(%o1)                             2 f1 + 2 e1
(%i2) ```
Run Example
```elem ([2,a,b], x*y+x+y, [x, y]);
resolvante
generale

NOTE: To compile the system do
define: warning: redefining the built-in function resolvante_produit_sym
define: warning: redefining the built-in function resolvante_unitaire
define: warning: redefining the built-in function resolvante_alternee1
define: warning: redefining the built-in function resolvante_klein
define: warning: redefining the built-in function resolvante_klein3
define: warning: redefining the built-in function resolvante_vierer
define: warning: redefining the built-in function resolvante_diedrale
define: warning: redefining the built-in function resolvante_bipartite
(%o1)                               b + 2 a
(%i2) elem ([2,a],x*y+x+y, [x,y]);
(%o2)                              e2 + 2 a
(%i3) elem ([2],x*y+x+y,[x,y]);
(%o3)                              e2 + 2 e1
(%i4) elem ([2],elem ([3,E1xy,E2xy],x*y+x+y+u*v,[x,y]), [u,v]);
(%o4)                         E2xy + e2 + 2 E1xy
(%i5) multi_elem ([[2, e1, e2], [2, f1, f2]], a*b + a^2 + (x+y)^2,[[x, y], [a, b]]);
2              2
(%o5)                      - f2 + f1  - 2 e2 + 2 e1
(%i6) multi_elem ([[2, ex1, ex2], [2, ey1, ey2]], (x1+x2) + (y1+y2)^2,[[x1,x2], [y1,y2]]);
2
(%o6)                      - 2 ey2 + 2 ey1  + 2 ex1
(%i7) ```

### Related Help

Help for Multi_elem